The present invention relates to radio wave receiving apparatus of which antenna resolution is improved by using a transfer function in azimuthal frequency domain of an antenna pattern.
When observing target objects for example in using a radar, a method has been generally used in which the pointing direction of an antenna beam is changed for example by rotating the antenna to receive radio waves from the respective azimuths pointed to by the antenna beam, so as to observe the intensity of the received radio wave (antenna response) with respect to the azimuths. In doing so, the use of an antenna with a narrower beamwidth results in an antenna response approximating the distribution of the radio wave sources and hence improves the azimuth resolution of the radar. To improve antenna resolution in the conventional art thus means to obtain an antenna response more closely approximating the distribution of the radio wave sources. Although another method is also known such as in a synthetic aperture radar where antenna resolution is improved by subjecting the received radio wave to a signal processing, this method, too, intends to obtain an antenna response approximating the distribution of the radio wave sources by achieving through the signal processing an equivalent effect as that of reducing the antenna beamwidth.
The above conventional technique for improving the antenna resolution is a method of indirectly obtaining the distribution of the radio wave sources from the antenna response and is with a problem that the distribution of the radio wave sources cannot be directly obtained. If there existed an antenna having its pattern represented by the Dirac delta function, the antenna response at such antenna would correspond to the response of the radio wave sources. It is known from the antenna theory, however, that an antenna having such pattern does not exist. Accordingly, since an actual antenna pattern has a finite beamwidth and sidelobes, there is a problem that the distribution of the observable radio wave sources is distorted by the antenna pattern.
To eliminate the above problems in the conventional case of obtaining the radio wave distribution from an antenna response, it is an object of the present invention to provide a radio wave receiving apparatus capable of directly obtaining the radio wave source distribution.
To solve the above problems, a radio wave receiving apparatus including an antenna for receiving radio waves and a means for moving the pointing direction of an antenna beam of the antenna toward directions for improving resolution is provided in accordance with the present invention, comprising: a means for a Fourier transform in respect of azimuth of a received electric field signal obtained from the antenna while moving the antenna beam; a means for a Fourier transform in respect of azimuth of a received electric field pattern in the presence of one point source of wave of the antenna; a means for dividing a signal resulting from the Fourier transform in respect of azimuth of the antenna-received electric field signal by a signal resulting from the Fourier transform in respect of azimuth of the received electric field pattern in the presence of one point source of wave of the antenna; a low-pass filter for subjecting the signal divided at the division means to low-pass filtering in respect of azimuthal frequency; a means for extracting exponential function components of the output signal of the low-pass filter; a band extension means for extending the output signal of the low-pass filter into an azimuthal frequency region beyond the cut-off frequency of the low-pass filter by using the extracted exponential function components; and a means for subjecting the signal extended by the band extension means to a Fourier inverse transform in respect of azimuth, the signal after the Fourier inverse transform being outputted as a final antenna output.
Supposing in a radio wave receiving apparatus where the pointing direction of antenna beam is moved, xcex8 is azimuth, g(xcex8) is an antenna pattern and f(xcex8) is a wave source distribution function, an antenna-received electric field e(xcex8) is given by the form of a convolutional integral as in the equation (1).
e(xcex8)=∫f(xc3x8)xc2x7g(xcex8xe2x88x92xc3x8)dxc3x8xe2x80x83xe2x80x83(1)
It should be noted that f(xc3x8) in the equation (1) is identical as the wave source distribution function f(xcex8) and xc3x8, representing an integral variable (an expedient variable in the integral equation), is of the same unit of azimuth as xcex8.
In general, the antenna pattern g(xcex8) is measured as an electric field received at the antenna in the presence of one point source of wave. Here supposing E(xcfx89), F(xcfx89), G(xcfx89) as the functions resulting from Fourier transform in respect of azimuth, respectively, of e(xcex8), f(xcex8), g(xcex8), i.e., as azimuthal frequency functions, the equation (1) may be represented by the form of a multiplication as in the following equation (2)
E(xcfx89)=F(xcfx89)xc2x7G(xcfx89)xe2x80x83xe2x80x83(2)
where G(xcfx89) is an azimuthal frequency function of antenna pattern, i.e., a transfer function in respect of azimuthal frequency of the antenna. Since the antenna pattern g(xcex8) is determined when the antenna to be used is decided, G(xcfx89) can be obtained by calculation from g(xcex8). Further, E(xcfx89) is an azimuthal frequency function of the antenna-received electric field e(xcex8) and can be obtained by calculation from a measured value of the electric field signal e(xcex8) received by the antenna at each pointing angle. Accordingly, E(xcfx89), G(xcfx89) are known and the azimuthal frequency distribution function F(xcfx89) of wave source can be obtained by
F(xcfx89)=E(xcfx89)/G(xcfx89)xe2x80x83xe2x80x83(3)
As described above, F(xcfx89) is the Fourier transform in respect of azimuth of the distribution function f(xcex8) of wave source. It is therefore possible to obtain the wave source distribution function f(xcex8) by a Fourier inverse transform in respect of azimuth of F(xcfx89) which is represented by the equation (3).
In the present invention, F(xcfx89) represented by the equation (3) is not directly subjected to Fourier inverse transform. Instead, it is processed of Fourier inverse transform after the following treatment. In particular, F(xcfx89) represented by the equation (3) is subjected to low-pass filtering through a low-pass filter in respect of azimuthal frequency and exponential function components are then extracted from the output signal of the low-pass filter. The output signal of the low-pass filter is then expanded into an azimuthal frequency region beyond the cut-off frequency of the low-pass filter on the basis of the extracted exponential function components so as to extend the band thereof. It then becomes possible to obtain a wave source distribution function f(xcex8) more closely approximating the wave source distribution by subjecting thus band-extended F(xcfx89) to Fourier inverse transform in respect of azimuth.
Accordingly, with the radio wave receiving apparatus having the above construction according to the present invention to which the above technique is applied, an equivalent resolution can be obtained as that of an antenna possessing its antenna pattern represented by the Dirac delta function and, since the band thereof is extended on the basis of exponential function components, the resolution can be furthermore improved based on the inversely proportional relationship between frequency band and resolution.
The extension of band on the basis of exponential function components will now be described. It is supposed in the present invention that F(xcfx89) can be expressed by the sum of xe2x80x9cmxe2x80x9d exponential functions which is represented by the following equation (4).
F(xcfx89)=xcexa3xcex1iexp(xcex2ixc2x7xcfx89)xe2x80x83xe2x80x83(4)
where the summation range of summation symbol xe2x80x9cxcexa3xe2x80x9d is i=l to i=m and the coefficients xcex1i, xcex2i are determined by the acquired data. Thereafter, the domain of data is expanded on the assumption that such relational expression holds also in regions outside the acquired range of the spatial frequencies xcfx89. Such technique for expanding domain is a type of extrapolation method. However, while the commonly used extrapolation is a general method which can be used even for unknown objects, the domain-expanding technique in the present invention is the technique limited to those objects which can be modeled when represented by the sum of point scattering objects such as radar scattering object. Accordingly, a superior advantage as compared to the commonly used extrapolation method can be obtained for the purpose of improving antenna resolution. This is because its objects are limited and data are effectively acquired by using an analysis method suitable for the model thereof so as to expand the domain.
The reason for performing the low-pass filtering of the divided output signal before extracting exponential function components at the exponential function component extraction means in the present invention is as follows. In particular, since a band in spatial frequency exists physically in the signal derived from Fourier transform of the received electric field pattern of antenna, components in a region exceeding such band cannot be possessed. Frequency components of regions beyond the above described band, however, are contained in the divided signal (radio wave source distribution spectrum) which is acquired by performing signal processing at the division means. This occurs due to the difference between the actual processing and theoretical processing. If the signal components of the regions beyond such band are used as they are to perform processing at the next stage (extracting of exponential functions), a signal degradation results. Accordingly, the signal components of regions beyond the above described band are removed by thus performing low-pass filtering at such stage, so as to prevent degradation of signal.